Question

tan30 × tan60 - tan 45​

Answer 1

☯ tan 30° × tan 60° - tan 45°

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━$

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$\underline{\bigstar\:\boldsymbol{According \;to \;the\: given \;Question\; :}}$

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• tan 30° ⟶ $\tt{\dfrac{1}{\sqrt{3}}}$

• tan 60° ⟶ $\tt{\sqrt{3}}$

• tan 45° ⟶ $\tt{1}$

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Therefore,

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:\tt{\dfrac{1}{\sqrt{3}}}\:\times\:{\sqrt{3}}\:-\:1$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:\tt{\dfrac{1}{\cancel{\sqrt{3}}}}\:\times\:{\cancel{\sqrt{3}}}\:-\:1$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:\tt{1\:-\:1}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:\tt{\underline{\boxed{\frak{\pink{r\:=\:0}}}}}\:\bigstar$

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$\:\:\:\:\:\:\:\therefore\:{\sf{\underline{Hence,\:the\:Value\:is\:{\textsf{\textbf{0}}}}}}.$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━$

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Know More:

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$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}$